Solving Systems of Linear Equations

Front

What is a system of linear equations?

Back

A set of two or more linear equations with the same variables.

Front

What does it mean for a system of equations to have one solution?

Back

The lines intersect at exactly one point, representing a unique solution.

Front

What does it mean for a system of equations to have no solution?

Back

The lines are parallel and never intersect, indicating that there is no point that satisfies both equations.

Front

What does it mean for a system of equations to have infinitely many solutions?

Back

The lines coincide, meaning they are the same line and have an infinite number of intersection points.

Front

How can you solve a system of linear equations graphically?

Back

By graphing each equation on the same coordinate plane and identifying the point(s) of intersection.

Front

What is the substitution method in solving systems of equations?

Back

A method where one equation is solved for one variable, and that expression is substituted into the other equation.

Front

What is the elimination method in solving systems of equations?

Back

A method where equations are added or subtracted to eliminate one variable, making it easier to solve for the other.

Front

What is the slope-intercept form of a linear equation?

Back

The form is y = mx + b, where m is the slope and b is the y-intercept.

Front

What is the point of intersection of two lines?

Back

The point where the two lines meet, representing the solution to the system of equations.

Front

How do you determine if two lines are parallel?

Back

If they have the same slope but different y-intercepts.